四元数线性代数方程组求解迭代算法研究

Research on iterative algorithm for solving quaternion system of linear algebraic equations

矩阵方程是高等数学中的常见工具,在物理、计算机等领域广泛运用。为进一步研究四元数线性代数方程组的迭代求解计算法,基于四元数线性代数方程性质分析,以矩阵一般式方程为例,对其进行等价实表示计算分析,通过构造R4J迭代和R4G-S迭代法,对矩阵一般式方程四元数线性代数方程组进行求解计算。

Matrix equation is a common tool in advanced mathematics,which is widely used in physics,computer and other fields.In order to further study the iterative calculation method of quaternion linear algebraic equations,based on the property analysis of quaternion linear algebraic equations,taking the matrix general equation as an example,the equivalent real representation is calculated and analyzed,and the quaternion linear algebraic equations of matrix general equation are solved by constructing R4J iterative method and R4G—S iterative method.